Compressed air hydraulic pump arrangements of this kind are used in many connections, e.g., to convert available compressed air energy into energy in the form of a much higher hydraulic pressure. An increase in pressure of from 6 to 600 kp/cm.sup.2 can readily be achieved, to drive different types of pneumatic press tools, jacks, and the like. Although such pump arrangements function satisfactorily in the main, they have certain drawbacks when higher demands are placed on their reliability and operational economy. For instance, their efficiency is not particularly high. Also, guidance of the air piston is relatively inaccurate, which means that the points at which the piston turns at the end of a working stroke varies in an undesirable manner. This variation in the turning positions of the piston can result in serious damage to the hydraulic pump, particularly if it is a two-stage pump working at high pressure.